Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

[TonyTheTiger20]

What about the other way? How much is losing to Wisconsin worth to St Cloud? Does the gain of 'opponents' and 'opponents-opponents' outweigh the hit to their own won-loss? Similar table?

Same calculation but different RPI value --

So losing to Wisconsin would be worth

0 (winning percentage in a loss) times 30%
plus .9375 (UW Win% taking out the SCSU games) times 24%
plus .4761 (UW OppWin%) times 46%

So that game RPI would be .4440

St. Cloud's unadjusted RPI is .4601. So their new RPI would be:

.4601 times (26-1=) 25
plus .4440
= 11.9465

Divided by 26 = .4595

Final answer: With a loss today, St. Cloud's RPI should be something like .4595, down from their current .4601.

Can you tell I was a math major???

This won't be exact, because after playing this game, Wisconsin's OppWin% is going to change (and everyone's else's factors are going to change, which will change everyone else's game RPIs... etc). But close enough for back of the envelope guesstimation. That's why we need a big ol' calculator to do RPI lol

EDIT: Checking my work modifying results on the BCI Pairwise calculator ( https://www.bcinterruption.com/boston-college-bc-eagles-womens-hockey/2017/11/4/16605602/2017-2018-ncaa-womens-hockey-pairwise-rankings-calculator ) looks like it'll be exactly .4586, which gives you an idea of how much peripheral results can affect things. Most teams' RPI is going to change today even though only UW and SCSU are playing.

[Eeyore]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

This won't be exact, because after playing this game, Wisconsin's OppWin% is going to change (and everyone's else's factors are going to change, which will change everyone else's game RPIs... etc). But close enough.

Will it? I know that the games you play against a team are dropped from their Win% for the calculation of your RPI. Based upon that, I had assumed that the games your opponent has played against their opponents (as well as the games you have played against their opponents) would be dropped from the calculation of your OppOppWin% component. That would seem like the consistent, and logical, way to do it, but I've never checked to see if it is. Done right, no game should affect more than one component of a team's RPI rating.

Then again, no sentence that starts, "If RPI were done right . . ." ends in anything but tears.

[TonyTheTiger20]

Based upon that, I had assumed that the games your opponent has played against their opponents (as well as the games you have played against their opponents) would be dropped from the calculation of your OppOppWin% component. That would seem like the consistent, and logical, way to do it, but I've never checked to see if it is.

It's actually not -- games are dropped from OppWin%, but not OppOppWin%.

From the RPI wiki:

The OWP is calculated by taking the average of the WP's for each of the team's opponents with the requirement that all games against the team in question are removed from the calculation. Continuing from the example above, assume Syracuse has played one other game and lost, while Cincinnati has played two other teams and won. The team in question has played Syracuse twice and therefore Syracuse must be counted twice. Thus the OWP of the team is (0/1 + 0/1 + 2/2) / 3 (number of opponents – Syracuse, Syracuse, Cincinnati). OWP = 0.3333

The OOWP is calculated by taking the average of each Opponent's OWP. Note that the team in question is part of the team's OOWP. In fact, the most re-occurring opponent of your opponents is the team in question.

[Eeyore]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

It's actually not -- games are dropped from OppWin%, but not OppOppWin%.

facepalm

[TonyTheTiger20]

facepalm

Hahaha

[Eeyore]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

So, does OppOppWin% include the games that opponent has played against its opponents, or is it the average of your opponents' OppWin% as calculated for the second component of their own RPI?

[robertearle]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

The RPI page shows both the 'unadjusted' and 'adjusted' values. So, we'll see the unadjusted go down a bit for UW, but the adjusted not change? This is going to be interesting...

Wisconsin's unadjusted went from .6417 to .6421, adjusted went from .6655 to .6650. (I had written down their 'before' numbers this AM)

(St Cloud from .4601 to .4586)

[vicb]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

.......
(St Cloud from .4601 to .4586)

.......
Final answer: With a loss today, St. Cloud's RPI should be something like .4595, down from their current .4601.

Can you tell I was a math major???

........

.4586 is almost something like .4595

[TonyTheTiger20]

So, does OppOppWin% include the games that opponent has played against its opponents, or is it the average of your opponents' OppWin% as calculated for the second component of their own RPI?

It's the latter -- this is great, I went through the exact mental exercise you're going through a few years ago when I first built my calculator lol

[TonyTheTiger20]

.4586 is almost something like .4595

Well my math check using the RPI calculator was spot on at least!

[Eeyore]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

It's the latter -- this is great, I went through the exact mental exercise you're going through a few years ago when I first built my calculator lol

One notable element in the way that OppWin% and OppOppWin% is calculated is that those values will be will be exactly .500 for all of your regular season conference games. Every win counted in either component will be balanced by a loss. All of the difference in the values comes from nonconference and playoff games.

[Quiet Riot]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

one notable element in the way that oppwin% and oppoppwin% is calculated is that those values will be will be exactly .500 for all of your regular season conference games. Every win counted in either component will be balanced by a loss. All of the difference in the values comes from nonconference and playoff games.

you math geeks are making my head spin

[Timothy A]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

So what are the geeks saying the numbers look like this week?

[dd17]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

you math geeks are making my head spin

I am dizzy. I know its all math but its wacky how OSU can be so high when they dont have a single win against a top-9 team and have lost to teams at 29 and 31? Sometimes math just does not add up for me.

[TonyTheTiger20]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

Someone mentioned Conference RPI in another thread. Here's everyone's RPI plotted out by conference on a chart: